000			04210nam a22004815i 4500
001			978-1-4614-1521-3
003			DE-He213
005			20140220083242.0
007			cr nn 008mamaa
008			111111s2012 xxu| s |||| 0|eng d
020			_a9781461415213 _9978-1-4614-1521-3
024	7		_a10.1007/978-1-4614-1521-3 _2doi
050		4	_aQA329-329.9
072		7	_aPBKF _2bicssc
072		7	_aMAT037000 _2bisacsh
082	0	4	_a515.724 _223
100	1		_aDragomir, Silvestru Sever. _eauthor.
245	1	0	_aOperator Inequalities of the Jensen, Čebyšev and Grüss Type _h[electronic resource] / _cby Silvestru Sever Dragomir.
250			_a1.
264		1	_aNew York, NY : _bSpringer New York, _c2012.
300			_aXII, 121p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringerBriefs in Mathematics, _x2191-8198
520			_aThe main aim of this book is to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces.   In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive selfadjoint operators as well as some results for the spectrum of this class of operators are presented. This text introduces the reader to the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators as well as the step functions of selfadjoint operators. The spectral decomposition for this class of operators, which play a central role in the rest of the book and its consequences are introduced. At the end of the chapter, some classical operator inequalities are presented as well. Recent new results that deal with different aspects of the famous Jensen operator inequality are explored through the second chapter. These include but are not limited to the operator version of the Dragomir-Ionescu inequality, the Slater type inequalities for operators and its inverses, Jensen’s inequality for twice differentiable functions whose second derivatives satisfy some upper and lower bound conditions and Jensen’s type inequalities for log-convex functions. Hermite-Hadamard’s type inequalities for convex functions and the corresponding results for operator convex functions are also presented. The Čebyšev, (Chebyshev) inequality that compares the integral/discrete mean of the product with the product of the integral/discrete means is famous in the literature devoted to Mathematical Inequalities. The sister inequality due to Grüss which provides error bounds for the magnitude of the difference between the integral mean of the product and the product of the integral means has also attracted much interest since it has been discovered in 1935 with more than 200 papers published so far. The last part of the book is devoted to the operator versions of these famous results for continuous functions of selfadjoint operators on complex Hilbert spaces. Various particular cases of interest and related results are presented as well. This book is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
650		0	_aMathematics.
650		0	_aOperator theory.
650		0	_aDifferential equations, partial.
650		0	_aDistribution (Probability theory).
650	1	4	_aMathematics.
650	2	4	_aOperator Theory.
650	2	4	_aPartial Differential Equations.
650	2	4	_aProbability Theory and Stochastic Processes.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461415206
830		0	_aSpringerBriefs in Mathematics, _x2191-8198
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-1521-3
912			_aZDB-2-SMA
999			_c101085 _d101085